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This paper introduces a new class of methods, which we call Möbius schemes, for the numerical solution of matrix Riccati differential equations. The approach is based on viewing the Riccati equation in its natural geometric setting, as a flow on the Grassmanian of m-dimensional subspaces of an (n + m)-dimensional vector space. Since the Grassmanians are compact differentiable manifolds, and the coefficients of the equation are assumed continuous, there are no singularities or intrinsicdoi:10.1137/s0036142996307946 fatcat:3jtah554tvampmkwavp6zs475e